Here \({\mathop {cap}({\mathcal {H}})}\)  is a measure of the capacity of the space \({\mathcal {H}}\) , such as its Vapnik-Chervonenkis (VC) dimension or the covering number (see [1]}), and \(O^*\)  can contain logarithmic terms and other terms of lower order.
The inequality above holds with high probability over the choice of the data sample.
